Approximately, the stopping distance of a car travelling at v km/h is given by the expression 5/24(v +(v^2)/32)m (v is measured in km/h), the 1st term representing the `reaction' distance of the driver and the second the distance through which the brakes are actually applied. Two cars are 35 m apart
when the 1st car, travelling at 45 km/h, makes an emergency stop. The driver of the second car has no prior warning of this hazard. Show that a collision must occur if the speed of a second car exceeds 71 km/h.